Factorise fully the following:a) x² + 2xb) 2x² - 6xc) 15x - 10x³d) 9x² + 3x³

Mathematics

1 answer:

Lostsunrise [7]3 years ago

6 0

Answer:

a) $x(x+2)$

b) $2x(x-3)$

c) $5x(3-2x^2)$

d) $3x^2(3+x)$

Step-by-step explanation:

a) $x^2+2x$

When factoring a binomial (a polynomial with two terms), what we will be looking for are the terms that are shared between them.

In this problem, it can be seen that both of these terms have and x. This means that we can factor it out to get

$x(x+2)$

b) $2x^2-6x$

What are the common terms here?

It can be seen that each of these share a 2x, so our factored form would be

$2x(x-3)$

c) $15x-10x^3$

What about this one?

The common factor of this one is 5x, so our factored form would be

$5x(3-2x^2)$

d) $9x^2+3x^3$

The common factor of this one is $3x^2$ , so our factored form would be

$3x^2(3+x)$

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Find the greatest common factor of 12a^3b, 16a^2b^2, and 36ab^3

scoundrel [369]

Answer:

The greatest common factor of $12 a^{3} b, 16 a^{2} b^{2}, 36 a b^{3} \text { is } 4 a b$

Solution:

To find the greatest common factor we have to find the prime factors of individual numbers and then find the number which is common to each given number.

Here the numbers are $12 a^{3} b, 16 a^{2} b^{2}, 36 a b^{3}$

Let us find out the prime factors of each number .

$\begin{array}{l}{\text { Prime factors of } 12 a^{3} b=2 \times 2 \times 3 \times a \times a \times a \times b} \\ {\text { Prime factors of } 16 a^{2} b^{2}=2 \times 2 \times 2 \times 2 \times a \times a \times a \times b \times b} \\ {\text { Prime factors of } 36 a b^{3}=2 \times 2 \times 3 \times 3 \times a \times b \times b \times b}\end{array}$